UNIT 102-3: BATTERIES, BULBS, AND CURRENT FLOW*

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1 Name St.No. - Date(YY/MM/DD) / / Section UNIT 102-3: BATTERIES, BULBS, AND CURRENT FLOW* OBJECTIVES We have in us somewhere knowledge... of the taste of strawberries... When we bite into a berry, we are ready to taste a certain kind of taste; if we taste something very different, we are surprised. It is this what we expect or what surprises us that tells us best what we really know. John Holt 1. To understand how a potential difference results in a current flow through a conductor. 2. To learn to design and wire simple circuits using batteries, wires, and switches. 3. To learn to use symbols to draw circuit diagrams. 4. To understand the use of ammeters and voltmeters for measuring current and voltage respectively. 5. To understand the relationship between the current flows and potential differences in series and parallel circuits. 6. To understand the concept of resistance. * Portions of this unit are based on research by Lillian C. McDermott & Peter S. Shaffer published in AJP 60, (1992).

2 Page 2 Physics for Life Sciences II Activity Guide SFU OVERVIEW 5 min In the following sessions, we are going to discover, extend, and apply theories about electric charge and potential difference to electric circuits. The study of circuits will prove to be one of the more practical parts of the whole physics course, since electric circuits form the backbone of much of twentieth century technology. Without circuits we wouldn't have electric lights, air conditioners, automobiles, cell phones, TV sets, dishwashers, computers, or DVD players. In the last unit you used a battery to establish a potential difference (or voltage) across two electrodes. Battery is a term applied to any device that generates an electrical potential difference from other forms of energy. The type of batteries you are using in this course are known as chemical batteries because they convert internal chemical energy into electrical energy. As a result of a potential difference, an electrical charge can be repelled from one terminal of the battery and attracted to the other. No charge can flow out of a battery unless there is a conducting material connected between its terminals. A flow of charge can cause a small light bulb to glow. In this unit, you are going to explore how charge originating in a battery flows in wires and bulbs. You will be asked to develop and explain some models that predict how the charge will flow in series and parallel circuits. You will also be asked to devise ways to test your models using a computer-based laboratory device that can measure the rate of flow of electrical charge through it or the potential difference between two points in a circuit.

3 Physics for Life Sciences II: Unit Batteries, Bulbs, & Current Flow Page 3 Authors: Priscilla Laws, John Luetzelschwab, David Sokoloff, & Ron Thornton SESSION ONE: CURRENT FLOW AND POTENTIAL DIFFERENCE 20 min 20 min What is Electric Current? The rate of flow of electric charge is more commonly called electric current. If charge is flowing through a conductor then the official mathematical definition of the average current is given by < i > ΔQ Δt Instantaneous current is defined in the usual way with a limit: i lim ΔQ Δt 0 Δt = dq dt 15 min 25 min The unit of current is called the ampere (A). One ampere represents the flow of one coulomb of charge through a conductor in a time interval of one second. Circuit Diagrams Now that you have been wiring circuits and drawing diagrams of them you may be getting tired of drawing pictures of the batteries, bulbs, and switches in your circuits. There are a series of symbols that have been created to represent circuits. These symbols will enable you to draw the nice neat square looking circuits that you see in physics textbooks. A few of the electric circuit symbols are shown below. and NSF. Modified at SFU by N. Alberding & S. Johnson, 2007, 2011.

4 Page 4 Physics for Life Sciences II Activity Guide SFU Battery Switch,! Single Pole Single Throw! (SPST) Bulb Wire Double Pole! Double Throw Switch! (DPDT) Single Pole! Double Throw Switch! (SPDT) Figure 3-3: Circuit Symbols Using these symbols, the standard circuit with a switch, bulb, wires, and battery can be represented as in the diagram below. Figure 3-4: A circuit sketch and corresponding diagram Activity 3-2: Drawing Circuit Diagrams (a) On the battery symbol, which line represents the positive terminal? The long one or the short one? Note: You should try to remember this convention for the battery polarity because some circuit elements, such as diodes, behave differently if the battery is turned around so it has opposite polarity. (b) Below is a photograph of a circuit that is built on a circuit construction kit. The wires are shown as blue and red lines. Draw a textbook circuit diagram of the circuit using the correct schematic symbols. (Each battery cell should use one battery symbol.)

5 Physics for Life Sciences II: Unit Batteries, Bulbs, & Current Flow Page 5 Authors: Priscilla Laws, John Luetzelschwab, David Sokoloff, & Ron Thornton "# $#!# 7 6!# %# and NSF. Modified at SFU by N. Alberding & S. Johnson, 2007, 2011.

6 Page 6 Physics for Life Sciences II Activity Guide SFU 30 min Developing a Model for Current Flow in a Circuit Several models for current flow in the circuit might be proposed. Four are diagrammed below. After you have discussed the various ideas you will be asked to figure out how to use one or more ammeters in your circuit to measure current and test your model. Model A There will be no electric current left to flow in the wire attached to the base of the battery Model B The electric current will travel in a direction toward the bulb in both wires Model C The direction of the current will be in the direction shown, but there will be less current in the return wire Model D The direction of the current will be as shown, and it will be the same in both wires Figure 3-5: Four alternative models for current flow Measuring Current with an Ammeter The ammeter is a device that measures current and displays it. It will allow you to explore the current flowing at different locations in an electric circuit. Current is typically measured in amperes (A) or milliamperes (ma). (1 ampere = 1000 milliamperes.) Usually we just refer to current as "amps" or "milliamps". To measure the current flowing through a part of the circuit, you must "insert" the ammeter at the point of interest. Disconnect the circuit, put in the ammeter, and reconnect with

7 Physics for Life Sciences II: Unit Batteries, Bulbs, & Current Flow Page 7 Authors: Priscilla Laws, John Luetzelschwab, David Sokoloff, & Ron Thornton it in place. For example, to measure the current in the righthand wire of the circuit in Figure 3-4 the ammeter could be connected as shown below (We will be using a circle with a capital A on it to represent an ammeter.): A + The ammeter measures both the magnitude and direction of current flow. A current flowing in through the positive (+) terminal and out through the negative ( ) terminal will be displayed as a positive current. Discovering Models for Current Flow that Work Discuss the various current flow models with your partners, and design measurements that will allow you to choose the model or models that best describe the actual current flowing through the circuit. (For example, to see if the current has a different magnitude or direction at different points in a circuit (e.g. model B or model C) you should connect two ammeters in various locations around the circuit. To investigate current flow models you will need: 1 ammeter, 0.25 A 1 digital multimeter 2 #14 bulbs with holder 1 D-cell battery and holder 1 SPST switch 6 alligator clip wires Describe your test (or tests) in the space below as well as your choice of the best model as a result of these tests. Activity 3-3: Picking a Model for Current Flow (a) Describe your tests. Include drawings of the circuits you used, showing where the ammeters were connected. and NSF. Modified at SFU by N. Alberding & S. Johnson, 2007, 2011.

8 Page 8 Physics for Life Sciences II Activity Guide SFU

9 Physics for Life Sciences II: Unit Batteries, Bulbs, & Current Flow Page 9 Authors: Priscilla Laws, John Luetzelschwab, David Sokoloff, & Ron Thornton (b) Which model or models seem to work? Is the current different at different locations in the circuit? Explain how you reached your conclusion based on your observations. 30 min Measuring Potential Difference with a Voltmeter Since a battery is a device that has a potential difference across its terminals, it is capable of giving energy to charges, which can then flow as a current through a circuit. Exploring the relationship between the potential differences in a circuit and the currents that flow in that circuit is a fundamental part of developing an understanding of how electrical circuits behave. Because potential differences are measured in volts, a potential difference is often informally referred to as a voltage. Let's measure voltage in a familiar circuit. Besides the ammeters you have been using so far to measure current, there are voltmeters to measure voltage. Figure 3-6 shows the symbols we will use to indicate a voltmeter and an ammeter V A! Figure 3-6: Symbols for a voltmeter (left) and an ammeter (right). The + sign on the voltmeter should be at the higher potential if the voltmeter reads positive. If the current in the ammeter flows from + to then the ammeter reads positive. and NSF. Modified at SFU by N. Alberding & S. Johnson, 2007, 2011.

10 V - + Page 10 Physics for Life Sciences II Activity Guide SFU Figure 3-7 shows a simple circuit with a battery, a bulb, and two voltmeters connected to measure the voltage across the battery and the voltage across the bulb. The circuit is drawn again symbolically on the right. Note that the word across is very descriptive of how the voltmeters are connected to measure voltage. + - V + - V V + V V Figure 3-7: Two voltmeters connected to measure the voltage across the battery and the bulb. To do the next few activities, you will need: V a D-cell alkaline battery and holder 2 #14 light bulbs a SPST switch a digital voltmeter an ammeter, 0.25 A A Digital Multimeter (DMM) used as a voltmeter and connected to a battery. Activity 3-4: Voltage Measurements in a Simple Circuit (a) First connect both the + and the - clips of the voltmeter to the same point in the circuit. Observe the reading. What do you conclude about the voltage when the leads are connected to each other (i.e. not across anything else)? (b) In the circuit in Figure 3-7, predict the voltage across the battery compared to the voltage across the bulb. Explain your predictions.

11 Physics for Life Sciences II: Unit Batteries, Bulbs, & Current Flow Page 11 Authors: Priscilla Laws, John Luetzelschwab, David Sokoloff, & Ron Thornton (c) Now test your prediction. Connect the circuit in Figure 3-7. Use the voltmeter to measure the voltage across the battery and then use it to measure the voltage across the bulb. Voltage across the Battery Voltage across the bulb What do you conclude about the voltage across the battery and the voltage across the bulb? Now let's measure voltage and current in your circuit at the same time. To do this, connect a voltmeter and an ammeter so that you are measuring the voltage across the battery and the current entering the bulb at the same time. (See Figure 3-8.) + - V V + + A + A - Figure 3-8: Meters connected to measure the voltage across the battery and the current through it. (The positive terminal of the battery is at the bottom.) Activity 3-5: Current and Voltage Measurements (a) Measure the voltage across the battery when the switch is closed and the light is lit. Enter the value in the table below in Activity 3-6d (b) Measure the current through the circuit when the switch is closed and the light is lit. Enter the value in the table below in Activity 3-6d and NSF. Modified at SFU by N. Alberding & S. Johnson, 2007, 2011.

12 Page 12 Physics for Life Sciences II Activity Guide SFU Now suppose you connect a second bulb, as shown in Figure V V V A + A + A - - Figure 3-9: Two bulbs connected in series with a voltmeter and an ammeter. Activity 3-6: Current and Voltage Measurements with Two Bulbs The predictions below should be completed before class. (a) How do you think the voltage across the battery will compare to that with only one bulb? (More, less or the same within measurement error?) (b) What do you think will happen to the brightness of the first bulb when you add a second bulb? Explain. (c) What will happen to the current drawn from the battery? Explain. (d) Connect a second bulb as shown, and test your predictions. Measure the voltage across both the bulbs and the current entering both bulbs with the switch closed and record in the table. Measurements 3-5 and 3-6 voltage current 1 bulb 2 bulbs (e) Did the addition of the second bulb seem to affect the battery voltage very much?

13 Physics for Life Sciences II: Unit Batteries, Bulbs, & Current Flow Page 13 Authors: Priscilla Laws, John Luetzelschwab, David Sokoloff, & Ron Thornton (f) Did the first bulb dim when you added the second one to the circuit? What happens to the current drawn from the battery? (g) Explain what you think the battery is doing and why the differences in voltage and current (if any) occur when a second bulb is added. (h) Is the battery more like a constant current source or a constant voltage source? Figure 3-10: A series circuit with one battery and two bulbs. (Note that the battery polarity is reversed from the previous figures. This is the conventional orientation for schematic diagrams.) Activity 3-7: More Current and Voltage Measurements with Two Bulbs (a) Explore the current flowing at various points in the series circuit of Use an ammeter and insert the ammeter at various places, removing the wires as necessary. to find The current entering Bulb A The current flowing from Bulb A to Bulb B The current leaving Bulb B Enter the data in the following table: Current flowing into Bulb A Current flowing from Bulb A to B Current flowing out of Bulb B and NSF. Modified at SFU by N. Alberding & S. Johnson, 2007, 2011.

14 Page 14 Physics for Life Sciences II Activity Guide SFU (b) Formulate a rule about the current flowing through the different parts of a series circuit. (c) Now measure the voltages across both bulbs and compare to the voltage of the battery. Element Voltage Bulb A Bulb B Battery (d) Formulate a rule about voltages across the elements of a series circuit.

15 Physics for Life Sciences II: Unit Batteries, Bulbs, & Current Flow Page 15 Authors: Priscilla Laws, John Luetzelschwab, David Sokoloff, & Ron Thornton SESSION TWO: SERIES AND PARALLEL CIRCUITS In the last session you saw that, when an electric current flows through a light bulb, the bulb lights. You also saw that to get a current to flow through a bulb you must connect the bulb in a complete circuit with a battery. A current will only flow when it has a complete path from the positive terminal of the battery, through the connecting wire to the bulb, through the bulb, through the connecting wire to the negative terminal of the battery, and through the battery. By measuring the current at different points in the simple circuit consisting of a bulb, a battery and connecting wires, you discovered a model for current flow, namely that the electric current was the same in all parts of the circuit. By measuring the current and voltage in this circuit and adding a second bulb, you also discovered that a battery supplies essentially the same voltage whether it is connected to one light bulb or two. 25 min In this session you will examine more complicated circuits than a single bulb connected to a single battery. You will compare the currents through different parts of these circuits by comparing the brightness of the bulbs, and also by measuring the currents with ammeters. Devising Your Own Rules to Explain Current Flow In the next series of exercises you will be asked to make a number of predictions and then to confirm your predictions with actual observations. Whenever your observations and predictions disagree you should try to develop new concepts about how circuits with batteries and bulbs actually work. In order to make the required observations you will need: A fresh D-cell alkaline battery in a holder 6 wires with alligator clip leads 4 #14 bulbs in sockets a SPST switch one ammeter, 0.25A Consider the two circuits shown in Figure Assume that all batteries are identical and that all bulbs are identical. What do you predict the relative brightness of the various bulbs will be? (Remember that you saw in the last session that the battery supplies essentially the same voltage whether there is one light bulb or two.) and NSF. Modified at SFU by N. Alberding & S. Johnson, 2007, 2011.

16 Page 16 Physics for Life Sciences II Activity Guide SFU (a) Figure 3-13: Two different circuits with identical components (a) a battery with a single bulb; (b) a battery with two bulbs (b) 25 min Current and Voltage In Parallel Circuits There are two basic ways to connect resistors (such as bulbs) in a circuit series and parallel. So far you have been dealing with bulbs wired in series. To make predictions involving more complicated circuits we need to have a more precise definition of series and parallel. These are summarized in the box below. Series Connection:! Two resistors are in series if they are connected so the same current that passes through one bulb passes through the other. Parallel Connection:! Two resistors are in parallel if their terminals are connected together so that at each junction one terminal of the one bulb is directly connected to the terminal of the other. i i junction 1 i 1 i 2 Series i Parallel i junction 2 Figure 3-14 Series and Parallel Connections Let's compare the behaviour of a circuit with two bulbs wired in parallel to the circuit with a single bulb. (See Figure 3-15.)

17 Physics for Life Sciences II: Unit Batteries, Bulbs, & Current Flow Page 17 Authors: Priscilla Laws, John Luetzelschwab, David Sokoloff, & Ron Thornton (a) (b) Figure 3-15: Two different circuits with identical components (a) a single bulb circuit and (b) a parallel circuit. Note that if bulbs A, D and E are identical, then the circuit in Figure 3-16 (below) is equivalent to circuit 3-15(a) when the switch is open (as shown) and equivalent to circuit 3-15(b) when the switch is closed. Figure 3-16: When the switch is open, only bulb D is connected to the battery. When the switch is closed, bulbs D and E are connected to the battery in parallel. Now, let's make some predictions about the currents in the branches of a parallel circuit. Activity 3-9: Predicting Currents in a Parallel Circuit (a) Predict the relative brightness of bulb A in Figure 3-15a with the brightness of bulbs D and E in Figure 3-15b. Which of the three bulbs will be the brightest? The dimmest? Explain the reasons for your predictions. (b) How do you think that closing the switch in Figure 3-16 will affect the current through bulb D? Explain. You can test your predictions in (a) and (b) by wiring up the circuit shown in Figure 3-16 and looking at what happens to the brightness of the bulbs as the switch is closed. and NSF. Modified at SFU by N. Alberding & S. Johnson, 2007, 2011.

18 Page 18 Physics for Life Sciences II Activity Guide SFU Note: Before you start the next activity make sure that (1) bulbs D and E have the same brightness when placed in series with the battery and (2) use a very fresh alkaline D-cell battery so it behaves like an ideal battery. Activity 3-10: Actual Currents in a Parallel Circuit (a) Wire up the circuit in Figure 3-16 and, by opening and closing the switch, describe what you observe to be the actual relative brightness of bulbs A, D and E. (Very small changes may be due to your non-ideal battery.) (b) Were the relative currents through bulbs A, D and E what you predicted? If not, can you now see why your prediction was incorrect? (c) Did closing the switch and connecting bulb E in parallel with bulb D significantly affect the current through bulb D? How do you know? What about the current from the battery? Is it always the same no matter what is connected to it, or does it change depending on the circuit? Is the current through the battery the same whether the switch in Figure 3-16 is open or closed? Make predictions based on your observations of the brightness of the bulbs, and test it using meters. Activity 3-11: Predicting Changes in Battery Current and Voltage (a) Based on your observations of the brightness of bulbs D and E in Activity 3-11, how do you think that closing the switch in Figure 3-16 will affect the current from the battery? Explain.

19 Physics for Life Sciences II: Unit Batteries, Bulbs, & Current Flow Page 19 Authors: Priscilla Laws, John Luetzelschwab, David Sokoloff, & Ron Thornton (b) Based on your observations in Activity 3-11, how do you think that closing the switch in Figure 3-16 will affect the current through bulb D? Explain. (c) Based on your observations in Activity 3-11, how do you think that closing the switch in Figure 3-16 will affect the voltage across the battery? Explain. and NSF. Modified at SFU by N. Alberding & S. Johnson, 2007, 2011.

20 Page 20 Physics for Life Sciences II Activity Guide SFU You can test your predictions by placing the voltmeter across the battery and inserting the ammeters in the circuit as shown in the following diagram. V A A! Figure 3-17: Meters connected to measure the current through the battery and the current through bulb D and the voltage of the battery when the switch is opened and closed. Activity 3-12: Observing Battery Voltage and Current (a) Collect data while closing and opening the switch as before. Measure the currents through the battery and through bulb D. How does closing the switch in the circuit affect the voltage across the battery? Current from Battery Current into Bulb D Battery Voltage Switch Open Switch Closed (b) Use your observations to formulate a rule to predict how the current through a battery will change as the number of bulbs connected in parallel increases. Can you explain why? (c) Compare your rule in (b) to the rule you stated in Activity 3-9 (e) relating the current through the battery to the total resistance of the circuit connected to the battery. Does the addition of more bulbs in parallel increase, decrease, or not change the total resistance of the circuit? (d) Explain your answer to (c) in terms of the number of paths available in the circuit for current flow.

21 Physics for Life Sciences II: Unit Batteries, Bulbs, & Current Flow Page 21 Authors: Priscilla Laws, John Luetzelschwab, David Sokoloff, & Ron Thornton (e) Does the amount of current through a battery appear to depend only on how many bulbs are in the circuit or does the arrangement of the bulbs matter also? (Don't forget your observations with bulbs in series in Activities 3-9 and 3-11!) Explain. (f) Does the total resistance of a circuit appear to depend only on how many bulbs are in the circuit or does the arrangement of the bulbs matter also? Explain. and NSF. Modified at SFU by N. Alberding & S. Johnson, 2007, 2011.

22 Page 22 Physics for Life Sciences II Activity Guide SFU 60 min More Complex Series and Parallel Circuits Applying your knowledge to a more complex circuit. Consider the circuit consisting of a battery and two bulbs, A and B, in series shown in Figure 3-18(a). What will happen if you add a third bulb, C, in parallel with bulb B (as shown in Figure 3-18(b))? You should be able to answer this question about the relative brightness of A, B, and C based on previous observations. The tough question is: how does the brightness of A change? Figure 3-18: Two different circuits with identical components Activity 3-13: Predictions About a More Complex Circuit (a) In Figure 3-18 (b) is A in series with B alone, with C alone, or with a combination of B and C? (You may want to go back to the definitions of series and parallel connections given earlier in this session.) (b) In Figure 3-18(b) are B and C in series or in parallel with each other? Explain.

23 Physics for Life Sciences II: Unit Batteries, Bulbs, & Current Flow Page 23 Authors: Priscilla Laws, John Luetzelschwab, David Sokoloff, & Ron Thornton (c) Is the resistance of the combination of B and C larger than, smaller than, or the same as B alone? Explain. (d) Is the resistance of the combination of bulbs A, B and C in Figure 3-18(b) larger than, smaller than or the same as the combination of bulbs A and B in Figure 3-18(a)? Explain. (e) Can you predict how the current through bulb A will change, if at all, when circuit 3-18 (a) is changed to 3-18 (b) (i.e. when bulb C is added in parallel to bulb B)? Explain the reasons for your answer. (f) When bulb C is added to the circuit, what will happen to the brightness of bulb A? Explain. (g) Finally, predict the relative rankings of brightness for all the bulbs, A, B, and C, after bulb C is added to the circuit. Explain the reasons for your answers. and NSF. Modified at SFU by N. Alberding & S. Johnson, 2007, 2011.

24 Page 24 Physics for Life Sciences II Activity Guide SFU Set up the circuit shown in Figure 3-19(a) below. You will need: 3 D-cell alkaline batteries 3 #14 light bulbs A SPST switch 2 ammeters, 0.25 A 1 digital voltmeter Convince yourself that this circuit is identical to Figure 3-18(a) when the switch is open (as shown) and to 3-18(b) when the switch, S, is closed. A V A Figure 3-19: (a) Circuit equivalent to Figure 3-18(a) when the switch is open, and to Figure 3-18(b) when the switch is closed. (b) Same circuit with ammeters connected to measure the current through bulb A and the current through bulb B and a voltmeter to measure the battery voltage. Now let's make some observations using this circuit. Activity 3-14: Observing a Complex Circuit (a) Observe the brightness of bulbs A and B when the switch is open, and then the brightness of the three bulbs when the switch is closed (when bulb C is added). Compare the brightness of bulb A with and without C added, and rank the brightness of bulbs A, B, and C with the switch closed. Brightest Dimmest Switch Open Switch Closed If two bulbs have equal brightness, list them in the same box. (b) If your observations and predictions of the brightness were not consistent, what changes do you need to make in your reasoning? Explain!

25 Physics for Life Sciences II: Unit Batteries, Bulbs, & Current Flow Page 25 Authors: Priscilla Laws, John Luetzelschwab, David Sokoloff, & Ron Thornton (c) Connect the two ammeters and the voltmeter as shown in Figure 3-19b. Measure what happens to the battery voltage and the voltage across bulb A. Also measure the current through bulb A and the current through bulb B when the switch is opened and closed. Record your measurements below: Measurement Switch Open Switch Closed Battery Voltage Bulb A Voltage Bulb B Voltage* Bulb A Current Bulb B Current *This can be deduced from the other voltage measurements. (d) What happens to the current from the battery and through bulb A when bulb C is added in parallel with bulb B? What do you conclude happens to the total resistance in the circuit? Explain. Power The brightness of a bulb depends on the product of the voltage across the bulb and the current through it. This product represents the power, or the electrical energy per unit time, used by the bulb: Power: P = VI If V is in volts and I in amperes then P is in watts.the electrical energy is converted to both heat and light so that the relationship of power to the brightness is not necessarily linear. Nevertheless, one should observe that the qualitative brightness and NSF. Modified at SFU by N. Alberding & S. Johnson, 2007, 2011.

26 Page 26 Physics for Life Sciences II Activity Guide SFU increases with the power if the light bulbs are of the same manufacture. 1 Activity 3-15: Calculate the power of the light bulbs (a) Use the voltage and current values in the table of 3-14 to calculate the power usage of the bulbs with both switch open and switch closed. Power Bulb A Bulb B Switch Open Switch Closed Bulb C (b) Does the power consumption of the bulbs correspond to the brightness ranking? 1 Note that commercial light bulbs are rated by the power they dissipate when used at the standard voltage, e.g., 110 V in N. America or 220 V in Europe. If a light bulb is used at a voltage for which it was not intended then its power dissipation will not be the rated value. For example, if a 60 W bulb bought in Europe is used in N. America, its power usage is much less than 60 W.

27 Physics for Life Sciences II: Unit Batteries, Bulbs, & Current Flow Page 27 Authors: Priscilla Laws, John Luetzelschwab, David Sokoloff, & Ron Thornton Series and Parallel Networks Let's look at a somewhat more complicated circuit to see how series and parallel parts of a complex circuit affect one another. The circuit is shown below.! Figure 3-20: A complex circuit with series and parallel connections. From your knowledge of current and voltage in parallel and series circuits you should be able to figure out what happens when the switch is closed. Activity 3-15: Series and Parallel Network (a) Predict the effect on the current in branch 1 of each of the following alterations in branch 2: (i) unscrewing bulb B, and (ii) closing switch S. (b) Predict the effect on the current in branch 2 of each of the following alterations in branch 1: (i) unscrewing bulb A, and (ii) adding another bulb in series with bulb A. (c) Connect the circuit in Figure 3-20, and observe the effect of each of the alterations in (a) and (b) on the brightness of each bulb. Record your observations for each case. and NSF. Modified at SFU by N. Alberding & S. Johnson, 2007, 2011.

28 Page 28 Physics for Life Sciences II Activity Guide SFU (d) Compare your results with your predictions. How do you account for any differences between your predictions and observations? (e) In this circuit, two parallel branches are connected across a battery. What do you conclude about the effect of changes in one parallel branch on the current in the other?

29 Physics for Life Sciences II: Unit Batteries, Bulbs, & Current Flow Page 29 Authors: Priscilla Laws, John Luetzelschwab, David Sokoloff, & Ron Thornton SESSION THREE: OHM S LAW & KIRCHHOFF'S LAWS Jimmy's Garage I need a new battery but its terminal potential needs to be at least 12 Joules per Coulomb with an internal resistance no greater than 0.1 Ohms and a capacity of 100 Amp-hours. And would you have something with a transient suppression of 10,000 Volts per second? 20 min When a battery is fresh, the voltage marked on it is actually a measure of the electrical potential difference between its terminals. Voltage is an informal term for potential difference. If you want to talk to physicists you should refer to potential difference. Communicating with a sales person at the local store is another story. There you would probably refer to voltage. We will use the two terms interchangeably. Let's explore potential differences in series and parallel circuits, and see if you can develop rules to describe its behaviour as we did earlier for currents. How do the potential differences of batteries add when the batteries are connected in series or parallel? Figure 3-11 shows a single battery, two batteries identical to it connected in series, and then two batteries identical to it connected in parallel. Figure 3-11: Identical batteries: (a) single, (b) two connected in series and (c) two connected in parallel. You can measure potential differences with a voltmeter connected as shown in Figure and NSF. Modified at SFU by N. Alberding & S. Johnson, 2007, 2011.

30 Page 30 Physics for Life Sciences II Activity Guide SFU V V V V V Figure 3-12: Voltmeters connected to measure the potential difference across (a) a single battery, (b) a single battery and two batteries connected in series, and (c) a single battery and two batteries connected in parallel. Activity 3-12: Combinations of Batteries (a) Predict the voltage for each combination of batteries in Fig Write you prediction beside the meter symbols. (b) Measure the voltages you predicted and write them below the predicted values on the figure. Using a Multimeter A digital multimeter (DMM) is a device that can be used to measure either current, voltage or resistance depending on how it is set up. We have already used one to measure voltage and current. The following activity will give you some practice in using it as an ohmmeter. You will need: A digital multimeter A D-cell alkaline battery w/ holder A SPST switch 4 alligator clip wires 1 resistor, 10 Ω V A! A MA COM V! MA Figure 3-16: Diagram of a typical digital multimeter that can be used to measure resistances, currents, and voltages

31 Physics for Life Sciences II: Unit Batteries, Bulbs, & Current Flow Page 31 Authors: Priscilla Laws, John Luetzelschwab, David Sokoloff, & Ron Thornton By putting the input leads (red for positive, black for negative) into the proper receptacles and setting the dial correctly, you can measure resistances (Ω) as well as direct-current voltages (DCV) and currents (DCA). Figure 3-17 shows two simple circuits to remind you how to take voltage and current readings with the multimeter which here acts as a voltmeter on the left and as an ammeter on the right. A 10! 10! V Figure 3-17: Simple circuits for using a multimeter to measure voltage and current. Uncertainty of Multimeter Measurements There are two sources of error to consider when measuring with a multimeter: 1. The effect of the meter on the circuit being measured and the consequent deviation of the value measured from what it was without the meter connected and 2. The possible error in calibration and the sensitivity of the meter s digital reading. Voltage Measurements Digital multimeters are usually designed so that very little current flows through them while they are being used. The technical jargon for this is high input impedance which means in practice that it acts like a very large resistor. Most digital multimeters can be assumed to have an input impedance of 1 MΩ or 10 MΩ. Thus if you measure the potential difference across a component with resistance comparable to the meter s then the effect of the parallel resistance of the meter should be considered. For components whose resistances are much smaller, then one can ignore the meter s effective resistance. The meter reading is subject to uncertainty caused by two influences: (1) the calibration of the meter and (2) the digitization error of the numerical reading. Normally calibration error is expressed as a percentage of the value. The digitization error is usually expressed as a ± range on the last digit. For example the technical specifications of our Meterman 33XR multimeters state that for DC voltage measurements the error is ±(0.7% + 1 digit) and NSF. Modified at SFU by N. Alberding & S. Johnson, 2007, 2011.

32 Page 32 Physics for Life Sciences II Activity Guide SFU One calculates the uncertainty as 0.7% of the reading plus one digit in rightmost digit of the reading. For example 2.47 V would have an error of ±0.7% 2.47 V = ±0.02 V added to ±0.01 V resulting in a total error of ±0.03 V. (We do not add these two contributions in quadrature.) Current Measurements Current measurements need to have the meter inserted in series with the circuit elements. Digital multimeters are apt to have a significant resistance compared to the other circuit elements, and the amount of resistance depends on the scale setting. For higher currents such as around 1 A the resistance could be a few ohms, but for milliampere ranges internal resistances could be as high as a kω. (Sometimes this is specified as voltage burden because there s an unwanted voltage across the meter while it s being used.) The result is that the meter causes the current being measured to be smaller than it would be without the meter. The error on current measurements depends on the scale. For most scales it is listed as ±(1%+1digit) for the 33XR Meterman DMM Resistance Measurements Resistance measurements combine both voltage and current measurement. A meter has to provide a voltage and measure the current for that voltage and then presents the ratio of voltage to current as the resistance value. Because the meter has to provide an exact voltage across the component being measured it s important to ensure that no other sources of voltage are connected which would interfere with the measurement. Similarly, the current from the meter must flow only through the component being measured. Therefore, the component must be disconnected from any other circuit element while the resistance is being measured. If the component is being tested in circuit, at least one end must be disconnected while measuring its resistance. While you re measuring the resistance of something you must make sure that it is not connected to anything else. Even having your fingers touching the leads can cause an erroneous measurement due to the body s resistance in parallel. Because both voltage and current are involved in measuring resistance, it is normal that the uncertainty is somewhat more than that for voltage or current. Most scales have a listed error of ±(1%+4 digits) for the 33XR Meterman DMM. AC/DC Both current and voltage functions of a multimeter have alternating current and direct current scales. Most of our measurements should use the direct current setting. If you get reading of almost zero when you expect a larger

33 Physics for Life Sciences II: Unit Batteries, Bulbs, & Current Flow Page 33 Authors: Priscilla Laws, John Luetzelschwab, David Sokoloff, & Ron Thornton value, then check if the meter is set on AC instead of DC. The specified error on AC measurements is typically larger than for DC measurements. Other Measurements Many DMMs have the ability to make various other measurements depending on the model. Some can measure frequency, capacitance, temperature, inductance or transistor current amplification. These may be very useful in some situations, but the three basic measurements are essential and should be mastered first. Activity 3-15: Using a Multimeter (a) Set up the circuit shown in Figure 3-17 with the switch open. Figure out what settings you need to use to measure the actual resistance of the "10Ω" resistor. Record your measured value below. (b) Now close the switch and measure the actual resistance of the 10Ω resistor again. Is your result different? If so, what do you think is the cause of this difference? Ohm s Law: Relating Current, Potential Difference and Resistance You have already seen on several occasions that there is only a potential difference across a bulb when there is a current flowing through the bulb. In this activity we are going to use a resistor and compare its characteristics to a light bulb. Resistors are designed to have the same resistance value no matter how much current is passing through. How does the potential difference across a resistor depend on the current through it? In order to explore this, you will need the following: 2 digital multimeters 4 D-cell alkaline batteries with holders 1 resistor, 68 Ω 1 SPST switch and NSF. Modified at SFU by N. Alberding & S. Johnson, 2007, 2011.

34 Page 34 Physics for Life Sciences II Activity Guide SFU 1 to 4 cells Use 1 to 4 batteries to vary the voltage, ΔV applied to a resistor. After measuring I and ΔV, plot the I vs ΔV graph for each. A graph of I vs. ΔV is called the characteristic curve and the resistance is the inverse of its slope. Activity 3-16 Experimental Relationship of I and ΔV a) Set up a circuit to test your prediction by placing the resistor in series with one, two, three and then four batteries. Set up the multimeters as a voltmeter and ammeter to measure the voltage across the resistor and the current through it. Carefully describe your procedures and sketch your circuit diagram. b) Record your data for I vs ΔV in the table below. Record values and uncertainties. Number of Batteries ΔV (Volts) I (Amps) c) Using a spreadsheet create a graph of I vs ΔV for both resistor. Draw a line through the points that starts at 0,0. Submit your graphs to WebCT. Ohm's Law and Resistance The relationship between potential difference and current which you have observed for a resistor is known as Ohm's law. To put this law in its normal form, we must now define the quantity known as resistance. Resistance is defined by:

35 Physics for Life Sciences II: Unit Batteries, Bulbs, & Current Flow Page 35 Authors: Priscilla Laws, John Luetzelschwab, David Sokoloff, & Ron Thornton!!! R ΔV/I If potential difference (ΔV ) is measured in volts and current (I) is measured in amperes, then the unit of resistance (R) is the ohm, which is usually represented by the Greek capital letter Ω, "omega." Activity 3-17: Statement of Ohm's Law a) State the mathematical relationship found in Activity 3-16 between potential difference and current for a resistor in terms of ΔV, I, and R. b) Based on your graph, what can you say about the value of R for a resistor is it constant or does it change as the current through the resistor changes? Explain. c) From the slope of your graph, what is the experimentally determined value of the resistance of your resistor in ohms? How does this agree with the rated value of the resistor? d) Complete the famous pre-exam rhyme used by countless introductory physics students throughout the English speaking world: Twinkle, twinkle little star, V equals times Note: Some circuit elements do not obey Ohm's law. The definition for resistance is still the same, but, as with a light bulb, the resistance changes because of temperature changes resulting from the flow of current. Circuit elements which follow Ohm's law over a wide range of conditions--like resistors--are said to be ohmic, while circuit elements which do not--like a light bulb--are nonohmic. and NSF. Modified at SFU by N. Alberding & S. Johnson, 2007, 2011.

36 Page 36 Physics for Life Sciences II Activity Guide SFU Resistance and Its Measurement In the series of observations you have been making with batteries and bulbs it is clear that electrical energy is being transferred to light and heat energy inside a bulb, so that even though all the current returns to the battery after flowing through the bulb, the charges have lost potential energy. We say that when electrical potential energy is lost in part of a circuit, such as it is in the bulb, it is because that part of the circuit offers resistance to the flow of electric current. A battery causes charge to flow in a circuit. The electrical resistance to the flow of charge can be compared to the mechanical resistance offered by the pegs and the barrier in a mechanical model depicted by a ramp with balls travelling down it as described in Unit 22. A light bulb is one kind of electrical resistance. Another common kind is provided by a resistor manufactured to provide a constant resistance in electrical circuits. Resistors are the most standard sources of resistance used in electrical circuits for several reasons. A light bulb has a resistance which increases with temperature and current and thus doesn't make a good circuit element when quantitative attributes are important. The resistance of resistors doesn't vary with the amount of current passing through them. Resistors is that they are inexpensive to manufacture and can be produced with low or high resistances. A typical resistor contains a form of carbon, known as graphite, suspended in a hard glue binder. It usually is surrounded by a plastic case with a colour code painted on it. It is instructive to look at samples of resistors that have been cut down the middle as shown in the diagram below. Figure 3-18: A cutaway view of a resistor

37 Physics for Life Sciences II: Unit Batteries, Bulbs, & Current Flow Page 37 Authors: Priscilla Laws, John Luetzelschwab, David Sokoloff, & Ron Thornton As you found in the previous activity on Ohm s Law, a simple equation can be used to define electrical resistance in terms of of potential difference, ΔV, across it and the current, I, through it. It is!!! R ΔV/I A resistor is usually marked with coloured bands to signify its resistance value in ohms.!"#$#%&'()&*&+'()&," -#%(.(/0,(,$1$% 2 3+*%$4*$"'!"#"$%&'(')*%%%%%%%%%%%%%%+)($",("-*%%%%%%.%/-*'0 0"(1-* #'(! (8& *':; *-! < '*8;#- 49 < = >-((': 429 =? #*--; 7()- B 1"'(-$ 42A B C D #*-> :E"$- &'501"(&'(="**&>(?50,($0,$65%"#(@AB( #4"6('"*$5?$*$%=( %&*"'506"7 '5%$01 '",(8(/9 1&*,(8(:9 #$*;"'(8(-<9 0&0"(8(/<9 For example, a resistor with bands of yellow-violet-red-silver has a value of: ± 10% Ω or 4.7 kω. Suppose you have finally graduated and taken a job as a quality control inspector for a company that makes resistors. Your task is to determine the rated resistance in ohms of a batch of five resistors and then check your decoding skills by measuring the resistance with a digital multimeter. For this activity you ll need: and NSF. Modified at SFU by N. Alberding & S. Johnson, 2007, 2011.

38 Page 38 Physics for Life Sciences II Activity Guide SFU A digital multimeter 5 assorted colour-coded resistors Activity 3-18: Decoding and Measuring Resistors a) Decode the 3 resistors and write their colour codes and Coded R values in the first two columns of the following table. Colour Sequence Coded R Ω Measured R Ω Calculated Percent Difference Percent Tolerance Within rated tolerance? Yes No b) Measure the resistance of each of your resistors with the multimeter. Fill in the values in the third column of the table above. (Include uncertainties.) c) Calculate the percent difference between the coded R and the measured R for each resistor using the following formula: coded R measured R percent difference = 100% coded R {\rm percent~difference} = { {{\rm coded~} R - {\rm measured~}r} \over { {\rm coded~}r} }\times 100\% Record this result for each resistor in the fourth column. d) Record the percent tolerance of each resistor in the fifth column. e) Are your resistor values correct within the rated tolerance values? Record your results in the last column and comment on whether this resistor manufacturer did a good job below. Resistors in Parallel and Series The resistance of a wire is directly proportional to length. The resistance also depends on the cross-sectional area of the wire. It is possible to control the R-value of a wire fairly precisely by varying these quantities.

39 Physics for Life Sciences II: Unit Batteries, Bulbs, & Current Flow Page 39 Authors: Priscilla Laws, John Luetzelschwab, David Sokoloff, & Ron Thornton Several identical resistors can be wired in series to increase their effective length and in parallel to increase their effective crosssectional area as shown in the next diagram. Figure 3-19: Resistors wired in series and in parallel In order to test your predictions and do some further exploration of equivalent resistances of different combinations of resistors you will need the following 2 resistors, ~100 Ω 2 resistors, ~220 Ω 2 resistors, ~330 Ω 1 digital multimeter 6 connecting wires with alligator clips Using the items listed above, you will devise a way to measure the equivalent resistance when three or more resistors are wired in series. Activity 3-19: Resistances for Series Wiring (a) If you have three different resistors, what do you think the equivalent resistance to the flow of electrical current will be if the resistors are wired in series? Explain the reasons for your prediction based on your previous observations with batteries and bulbs. (b) Compare the calculated and measured values of equivalent resistance of the series network as follows: Write down the measured values of each of the three resistors: R1 = Ω R2 = Ω and NSF. Modified at SFU by N. Alberding & S. Johnson, 2007, 2011.

40 Page 40 Physics for Life Sciences II Activity Guide SFU R3 = Ω Describe the method you are using to predict the equivalent resistance and calculate the predicted R value: Predicted Req = Ω (c) Draw a diagram for the resistance network for the three different resistors wired in series. Mark the measured values of the three resistances on your diagram. (d) Measure the actual resistance of the series resistor network and record the value: Measured Req = Ω (e) How does this value compare with the one you calculated? (f) On the basis of your experimental results, devise a general mathematical equation that describes the equivalent resistance when n resistors are wired in series. Use the notation R eq to represent the equivalent resistance and R 1, R 2, R 3,...R n to represent the values of the individual resistors.

41 Physics for Life Sciences II: Unit Batteries, Bulbs, & Current Flow Page 41 Authors: Priscilla Laws, John Luetzelschwab, David Sokoloff, & Ron Thornton Now you re going to devise a way to measure the equivalent resistance when two or more resistors are wired in parallel, Draw a symbolic diagram for each of the wiring configurations you use. Activity 3-110: Resistances for Parallel Wiring (a) If you have two identical resistors what to you think the resistance to the flow of electrical current will be if the resistors are wired in parallel? Explain the reasons for your prediction. (b) Pick out two resistors with an identical colour code and draw a diagram for these two resistors wired in parallel. Label the diagram with the measured values R 1 (measured) and R 2 (measured). Predict the equivalent resistance of the parallel circuit and record your prediction below. Measure the value of the equivalent resistance of the network. Explain your reasoning and show your calculations in the space below. and NSF. Modified at SFU by N. Alberding & S. Johnson, 2007, 2011.